In JP6-37931A, when a downshift is performed in an automatic transmission while a vehicle is in a coasting state, a comparatively high oil pressure is supplied to an engagement side frictional engagement element to accelerate an engagement side piston stroke. A low oil pressure (to be referred to hereafter as an initial oil pressure) is then supplied to end the stroke. The oil pressure of the engagement side frictional engagement element is then raised from the initial oil pressure such that the downshift in the automatic transmission is completed through a torque phase and an inertia phase.